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mynameisfunk

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In summary: According to the definition provided, an "interaction term" refers to the product of two or more variables, such as C X1 X2 in Model_A and R Y1 X2 in Model_B. A "nested model" refers to a model that can be written as a subset of a larger model, with the same variables but fewer terms. In summary, the question is asking whether a new model, which includes an interaction term between a collapsed categorical variable and a continuous variable, can be considered nested within the original model with an interaction term between the original categorical variable and continuous variable.

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mynameisfunk

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Stephen Tashi

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You might mean that you are dealing with a quadratic model of the form Model_A: Z = A X1 + B X2 + C X1 X2 + D with variables X1, X and another model of the form Model_B: Z = P Y1 + Q X2 + R Y1 X2 + S with variables Y1 and X2 where X2 is the same variable as in Model_A and Y1 is the function of X2 given by Y1 = 0 if X1 = 0 and Y1 = 1 otherwise.

The definition of "Model_B is nested within Model_A" might mean that there exists a way to write Model_A and model_B as quadratic models using the same set of variables such that Model_B expresses Z as a proper subset of the "terms" in Model_A. But does this also mean that a term (such as Q X2) that appears in Model_B has the same (perhaps unknown) constant coefficient as the corresponding term in Model_B (i.e. must P = Q in the previous example?).

A nested model is a statistical model in which one or more variables are included as a subset of another variable. This means that the included variables are dependent on the other variable and cannot be analyzed independently.

A non-nested model does not have any variables that are subsets of other variables, meaning that all variables are analyzed independently. In a nested model, the included variables are dependent on the other variable and cannot be analyzed independently.

Collapsing categorical variables in a nested model is important because it helps to reduce the complexity of the model by combining similar categories. This can improve the interpretability and accuracy of the model's results.

A model can be nested with itself before collapsing categorical variables by including the same variables at different levels of the model. For example, a variable representing different age groups can be included at both the individual level and the group level in a nested model.

One potential drawback of using a nested model with collapsed categorical variables is that it may oversimplify the relationships between variables and lead to biased results. Additionally, collapsing variables may result in loss of information and decrease the accuracy of the model's predictions.

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